Antenna diversity arrangement

ABSTRACT

An antenna diversity arrangement ( 200 ) comprises a plurality of antennas ( 204   a   , 204   b ) capable of forming a plurality of antenna beams. The amplitude and phase relationships between the signals driving each of the antennas ( 204   a   , 204   b ) are first determined for an arrangement where each antenna is replaced by a point source. The results of this analysis are then transformed by reference to the characteristics of the real antenna arrangement ( 200 ) to determine appropriate driving signals.  
     The resultant antenna diversity arrangements ( 200 ) can have antennas ( 204   a   , 204   b ) located arbitrarily close to one another with near-zero correlation between any pair of the antenna beams, thereby providing a compact and effective arrangement.

[0001] The present invention relates to an antenna diversity arrangementcomprising a plurality of antennas for providing angular diversity, andfurther relates to a wireless device incorporating such an antennadiversity arrangement and to a method of operating such an arrangement.

[0002] Antenna diversity is a well-known technique for mitigating theeffects of multipath propagation in a radio communication system. Whenthe signals received by two (or more) antennas are sufficientlydecorrelated it has been shown that narrowband diversity gains ofapproximately 10 dB can be achieved.

[0003] The spatial correlation of fields in a mobile radio environmentwas studied in A Statistical Theory of Mobile-Radio Reception, R. J.Clarke, Bell Systems Technical Journal, Volume 47 No. 6, pages 957 to1000. In this paper the well-known formula for the spatial envelopeauto-correlation coefficient ρ_(e) of a received vertically polarisedwave was shown to be given by

ρ_(e)=|ρ|² =J ₀(kx)  (1)

[0004] where ρ is the auto-correlation coefficient of the magnitude ofthe electric field, k is the wavenumber and x is the distance. Thisfunction is plotted in FIG. 1

[0005] In communication systems that employ diversity, such as DECT(Digital Enhanced Cordless Telecommunications), it is conventional toemploy two antennas to provide spatial diversity. Each antenna isdesigned to be omni-directional (at least for a cellular systememploying substantially circular cells) and independent of the otherantenna. This is achieved by separating the antennas by a large distance(which is required for good spatial decorrelation, as can be seen fromFIG. 1) and, if necessary, by detuning the unused antenna. However, thelarge separation between the antennas places restrictions on theequipment size. Further, the potential of a dual antenna system toachieve array gain (or directivity) is not realised.

[0006] By considering the antennas as an array, an angular diversitysystem can be designed in which a plurality of beams are generated froma plurality of antennas. The directivity of the beams provides enhancedcoverage while reducing delay spread (because of the reduced angularrange over which signals are transmitted) The use of array gain enhancescoverage, thereby further improving signal quality and coverage.

[0007] However, it has not hitherto been possible to design angulardiversity systems having arbitrarily closely spaced antennas whilemaintaining low correlation between the beams. For example, PCTapplication WO 99/55012 presents a diversity system having two antennasseparated by a third of a wavelength, with a 90° phase shift between thefeed voltages to the two antennas for the generation of directionalbeams. However, no account was taken of correlation coefficients in thedesign of this diversity system, nor of the fact that the antennas inthat system did not behave as ideal point sources, with the result thatthe behaviour of the system will not generally be optimum.

[0008] As an alternative to angular diversity, polarisation diversityhas been used with small antenna separations. However, differences inthe mean power of each polarisation cause degradation of the diversitygain. Also, there is no scope for realising coverage enhancement ordelay spread improvement.

[0009] An object of the present invention is to provide an antennadiversity arrangement having improved angular diversity performance fromantennas which can be arbitrarily closely spaced.

[0010] According to a first aspect of the present invention there isprovided a antenna diversity arrangement comprising a plurality ofantennas and means for feeding each of the plurality of antennas with asignal of suitable amplitude and phase to enable the generation of aplurality of antenna beams, wherein the correlation coefficient betweenany pair of beams is substantially zero.

[0011] According to a second aspect of the present invention there isprovided a wireless device incorporating an antenna diversityarrangement made in accordance with the present invention.

[0012] According to a third aspect of the present invention there isprovided a method of operating an antenna diversity arrangementcomprising a plurality of antennas, the method comprising feeding eachof the plurality of antennas with a signal of suitable amplitude andphase to enable the generation of a plurality of antenna beams, whereinthe correlation coefficient between any pair of beams is substantiallyzero.

[0013] The present invention is based on the realisation that an angulardiversity arrangement having zero envelope correlation coefficientbetween the antennas can readily be designed using ideal point sourcesof radiation separated by arbitrary distances. A practical realisation,for the same antenna separations, can then be obtained by appropriatetransformations to yield the required feed voltages for an arraycomprising dipole, monopole, helical or other antennas. The analysismethods presented here therefore enable the design of a wide range ofcompact antenna diversity arrangements, taking full account of mutualinteractions between the individual antennas.

[0014] Embodiments of the present invention will now be described, byway of example, with reference to the accompanying drawings, wherein:

[0015]FIG. 1 is a graph showing how the auto-correlation function forthe magnitude of the electric field at two points, |ρ|², varies withseparation in wavelengths, x/λ of the points;

[0016]FIG. 2 is a block schematic diagram of an antenna diversityarrangement;

[0017]FIG. 3 shows directional coverage of two oppositely directed beamscompared with an omni-directional beam;

[0018]FIG. 4 is a contour plot of the relationship between the maximumgain (in dB) of a two-element antenna array and the differential phaseshift Δ and electrical spacing kd of the antennas;

[0019]FIG. 5 is a contour plot of the relationship between the envelopecorrelation coefficient of a two-element antenna array and thedifferential phase shift Δ and electrical spacing kd of the antennas;

[0020]FIG. 6 is a graph showing the values of the differential phaseshift Δ and electrical spacing kd of two point sources which result inzero correlation between two beams;

[0021]FIG. 7 shows an azimuthal radiation pattern for a point sourcearray of two elements at 1890 MHz,

[0022]FIG. 8 shows azimuthal radiation patterns for an array of twolinear dipole elements, with both elements fed, at 1700 MHz (dashed),1890 MHz (solid) and 2080 MHz (chain dashed);

[0023]FIG. 9 is a Smith chart showing the impedance of one antenna of anarray of two linear dipoles over the frequency range 1700 to 2080 MHz;and

[0024]FIG. 10 shows azimuthal radiation patterns for an array of twolinear dipole elements, with one element loaded by a parasiticreactance, at 1700 MHz (dashed), 1890 MHz (solid) and 2080 MHz (chaindashed).

[0025]FIG. 2 illustrates an antenna diversity arrangement 200 which willbe used to describe an embodiment of the present invention (thearrangement will behave similarly for transmission and reception,according to the principle of reciprocity). The arrangement 200comprises an antenna feed 202 which carries the signal to betransmitted, at an appropriate frequency and power level, which signalis split and supplied to first and second antennas 204 a,204 b. Thesignal supplied to the second antenna 204 b is passed through a phaseshifter 206 which can shift the phase of the signal by up to ±180°, andmay also adjust the amplitude of the signal if required.

[0026] The desired radiation pattern from this two-element array is apair of identical but oppositely-directed and orthogonal beams (i.e.beams having zero or very small envelope auto-correlation coefficientρ_(e)). Together the beams provide omni-directional coverage, whileindividually they receive equal powers in a typical fading environment(where all azimuth angles of arrival are, on average, equally likely).

[0027]FIG. 3 shows an example of the directional coverage from such anarray. A base station 302 having an antenna diversity arrangement 200 isable to transmit and receive via an omni-directional beam 304, a firstdirectional beam 306 (shown dashed in FIG. 3) and a second directionalbeam 308 (shown chain dashed in FIG. 3). Hence, a mobile station 310which is out of range of the omni-directional beam 304 is able tocommunicate with the base station 302 via the first directional beam306.

[0028] The present invention will first be described in relation to anarray of two point sources of radiation, for which characteristics ofgain and correlation coefficient will be determined. It will then beshown how an array having desired characteristics can be implementedwith linear antennas. An example of the application of the presentinvention to a practical application will then be detailed.

[0029] Consider an array of point sources, all located in the horizontalplane. The far-field electric field E in the same plane is given by$\begin{matrix}{E = {\sum\limits_{n = 1}^{N}\quad {A_{n}^{j{({\Delta_{n} + {k\quad d_{n}{\cos {({\varphi - \varphi_{n}})}}}})}}}}} & (2)\end{matrix}$

[0030] where Δ_(n) is the phase and A_(n) is the amplitude of the n^(th)feed, d_(n) is the distance of the n^(th) source from the origin, andφ_(n) is the angle subtended between the x axis and a line from theorigin to the n^(th) source.

[0031] For a two-element embodiment, consider both antennas to belocated on the x axis (so that φ_(n)=0). In the first transmission mode,the first antenna 204 a is considered as the reference and the feed tothe second antenna 204 b has its amplitude and phase adjusted, causing adirectional beam to be formed in a particular direction. In the secondmode the relative amplitudes and phases are reversed, thereby causing adirectional beam in the opposite direction. For simplicity it will beassumed that the antennas are fed with equal amplitudes. The radiationpatterns of the two modes, E₁ and E₂ respectively, are therefore givenby

E ₁=1+e ^(j(Δ+kd cos φ))

E ₂ =e ^(jΔ) +e ^(jkd cos φ)  (3)

[0032] where d is equal to the distance between the two antennas 204a,204 b and Δ is the phase difference between the feeds of the twoantennas.

[0033] To enable radiation patterns to be compared they requirenormalisation. The appropriate normalisation relation is the innerproduct of the radiation patterns, given by

∫Ddφ=∫EE*dφ=2π  (4)

[0034] From the expressions for E₁ and E₂ in equation 3 above, it can bedetermined that

E ₁ E* ₁=2(1+cos(Δ+kd cos φ))

E ₂ E* ₂=2(1+cos(Δ−kd cos φ))  (5)

[0035] Hence, it can readily be shown that

∫E ₁ E* ₁ dφ=∫E ₂ E* ₂ dφ=4π(1+J ₀(kd)cos Δ)  (6)

[0036] Hence, using equation 4, it can be seen that both E₁ and E₂ canbe normalised by the factor $\begin{matrix}\frac{1}{\sqrt{2( {1 + {{J_{0}( {k\quad d} )}\cos \quad \Delta}} )}} & (7)\end{matrix}$

[0037] Combining equations 5 and 7 gives the power gain G of the secondbeam (which is the same as that of the first beam but in the oppositedirection) as $\begin{matrix}{{G(\varphi)} = \frac{1 + {\cos ( {\Delta - {k\quad d\quad \cos \quad \varphi}} )}}{1 + {{J_{0}( {k\quad d} )}\cos \quad \Delta}}} & (8)\end{matrix}$

[0038] For Δ and kd between 0 and 180°, the maximum gain occurs at φ=0for Δ>kd and at cos⁻¹(Δ/kd) elsewhere. FIG. 4 is a contour plot showinghow the maximum gain (in dB) depends on the differential phase shift Δand electrical spacing kd of the antennas 204 a,204 b. This demonstratesthat super-directivity is possible at very close antenna spacings.

[0039] However, it is also necessary for the beams to have a lowenvelope correlation coefficient ρ_(e). For the antenna diversityarrangement 200, comprising two antennas 204 a,204 b in a Rayleighfading environment, it was demonstrated in the paper by Clarke citedabove that this coefficient is given by $\begin{matrix}{\rho_{e} = \frac{{{\int_{\Omega}^{\quad}{( {{E_{1\quad \theta}E_{2\quad \theta}^{*}p_{\theta}}\quad + {X\quad E_{1\quad \varphi}E_{2\quad \varphi}^{*}p_{\varphi}}} )^{{- j}\quad k\quad \Delta \quad x}\quad {\Omega}}}}^{2}}{\int_{\Omega}^{\quad}{( {{E_{1\quad \theta}E_{1\quad \theta}^{*}p_{\theta}}\quad + {X\quad E_{1\quad \varphi}E_{1\quad \varphi}^{*}p_{\varphi}}} ){\Omega}{\int_{\Omega}^{\quad}{( {{E_{2\quad \theta}E_{2\quad \theta}^{*}p_{\theta}}\quad + {X\quad E_{2\quad \varphi}E_{2\quad \varphi}^{*}p_{\varphi}}} ){\Omega}}}}}} & (9)\end{matrix}$

[0040] where:

[0041] E_(θ) and E_(φ) are the complex electric field patterns of the θand φ polarisations respectively;

[0042] X is the cross-polar ratio P_(φ)/P_(θ), where P_(θ) and P_(φ) arethe powers that would be received by isotropic θ and φ polarisedantennas respectively in a multipath environment;

[0043] p_(θ) and p_(φ) are the angular density functions (angle ofarrival probability distributions) of the incoming θ and φ polarisedplane waves respectively; and

[0044] Δx is the difference in distance between waves incident at thetwo antennas 204 a,204 b (a function of angle).

[0045] Although the correlation coefficient ρ_(e) defined by equation 9is based on reception, it simplifies to an equation that is a functionof the incoming multipath and the complex radiation pattern. Byreciprocity, the equation is therefore equally applicable totransmission from the antenna diversity arrangement 200.

[0046] When the two antennas 204 a,204 b are considered as a singleantenna array, so the radiation patterns of the two antennas arereferred to the same point in space, Δx=0 and equation 9 simplifies to$\begin{matrix}{\rho_{e} = \frac{{{{\int_{\Omega}^{\quad}{E_{1\quad \theta}E_{2\quad \theta}^{*}p_{\theta}\quad {\Omega}}} + {X{\int_{\Omega}^{\quad}{E_{1\quad \varphi}E_{2\quad \varphi}^{*}p_{\varphi}\quad {\Omega}}}}}}^{2}}{\int_{\Omega}^{\quad}{( {{{E_{1\quad \theta}}^{2}p_{\theta}} + {X{E_{1\quad \varphi}}^{2}p_{\varphi}}} ){\Omega}{\int_{\Omega}^{\quad}{( {{{E_{2\theta}}^{2}p_{\theta}} + {X{E_{2\quad \varphi}}^{2}p_{\varphi}}} ){\Omega}}}}}} & (10)\end{matrix}$

[0047] It can clearly be seen from equations 9 and 10 that thecorrelation is a strong function of the orthogonality of thepolarisation states of each beam, albeit weighted by the angle ofarrival probability distribution. If the beams are orthogonal at allpoints in space, then the envelope correlation ρ_(e) will be zero andthe diversity performance will be optimised. The simplest configurationhaving this property is non-overlapping beams, although it is well knownthat orthogonality can be achieved with overlapping beams. Hence, eventhough the cross-polarisation and angle of arrival statistics areimportant parameters in determining the correlation coefficient ρ_(e),good insight into diversity performance can be obtained by studying thebeam orthogonality alone.

[0048] To evaluate the correlation coefficient ρ_(e) using the radiationpatterns defined in equations 3, it is necessary to evaluate E₁E*₂.Ignoring normalisation (since the normalising factors cancel out inequations 9 and 10),

E ₁ E* ₂=(1+e ^(jΔ) e ^(jkd cos φ))(e ^(jΔ) +e ^(jkd cos φ))*=2(cosΔ+cos(kd cos φ))  (11)

[0049] Integrating this expression over the xy plane, $\begin{matrix}{{\int{E_{1}E_{2}^{*}{\varphi}}} = {{2( {{\int_{0}^{2\quad \pi}{\cos \quad \Delta \quad {\varphi}}} + {\int_{0}^{2\quad \pi}{{\cos ( {k\quad d\quad \cos \quad \varphi} )}{\varphi}}}} )} = {4{\pi ( {{\cos \quad \Delta}\quad + {J_{0}( {k\quad d} )}} )}}}} & (12)\end{matrix}$

[0050] Assuming vertical polarisation alone from the point sources, sothat E_(1φ)=E_(2φ)=0, and a uniform angle of arrival probabilitydistribution (so that p_(θ) is a constant), the envelope correlationcoefficient ρ_(e) is obtained from equations 10, 12 and 6 as$\begin{matrix}{\rho_{e} = ( \frac{{\cos \quad \Delta} + {J_{0}( {k\quad d} )}}{1 + {{J_{0}( {k\quad d} )}\cos \quad \Delta}} )^{2}} & (13)\end{matrix}$

[0051]FIG. 5 is a contour plot showing how the envelope correlationcoefficient ρ_(e) depends on the differential phase shift Δ andelectrical spacing kd of the antennas. It can clearly be seen that thereis a significant region of very low ρ_(e), with ρ_(e)=0 whenΔ=cos⁻¹(−J₀(kd)).

[0052] It is possible to obtain completely decorrelated beams forantenna spacings down to zero (at least theoretically). FIG. 6 is agraph showing the values of differential phase shift Δ and electricalspacing kd which result in ρ_(e)=0, covering a wider range of electricalspacings than shown in FIG. 5. It can be seen that as the antennaseparation is reduced the required phase shift Δ tends towards 180°,while for electrical separations of greater than 120° there is a channelof low correlation coefficient when the mean phase difference Δ betweenthe feeds is approximately 90°.

[0053] It can be seen, by comparing FIGS. 4 and 5, that the conditionsfor orthogonal beams, low correlation and high gain are all consistentwith each other. This is to be expected, since these conditions canbroadly be summarised as minimum overlap between radiation patterns.

[0054] The derivation above related to idealised point sources ofradiation rather than practical antennas. It will now be demonstratedhow similar results can be obtained from vertically-orientated linearantennas, for example monopoles, dipoles or helices. The analysis hereis adapted from that commonly used for AM broadcast antennas, see forexample Matrix Method for Relating Base Current Ratios to Field Ratiosof AM Directional Stations, J. M. Westberg, IEEE Transactions onBroadcasting, Volume 35 No. 2, pages 172 to 175.

[0055] Consider a two-element antenna array 200. The voltages V andcurrents I at the feed points of each element of the array are relatedfrom simple circuit theory by

I ₁ =V ₁ Y ₁₁ +V ₂ Y ₁₂

I ₂ =V ₁ Y ₂₁ +V ₂ Y ₂₂  (14)

[0056] The far field radiation in the horizontal plane from avertically-orientated linear element is given by $\begin{matrix}{E_{\theta \quad z} = {{- j}\frac{\eta \quad k}{4\pi \quad r}^{{- \quad j}\quad k\quad r}{\int{{I_{z}(z)}{z}}}}} & (15)\end{matrix}$

[0057] where η is the impedance of free space, r is the radial distancefrom the centre of the element, and I_(z)(z) is the current distributionon the antenna 204 a,204 b (which is assumed to be linear in the zdirection).

[0058] For an array comprising a plurality of antennas 204 a,204 b, theradiation from each antenna can be written as

E _(n) =K∫I _(zn)(z)dz  (16)

[0059] where K represents the factor before the integral in equation 15,the subscript n represents the n^(th) element and I_(zn)(z) is theelemental current along the length of the n^(th) element.

[0060] Because antennas are linear systems, where the field at aparticular point in space is proportional to the input voltage orcurrent, equation 16 can be written as

E_(n)=C_(n)I_(n)  (17)

[0061] where I_(n) is the feed current of the n^(th) element.Substitution of equations 17 and 16 into equation 14 then gives$\begin{matrix}\begin{matrix}{{\frac{K}{C_{1}}{\int{{I_{z1}(z)}{z}}}} = {{V_{1}Y_{11}} + {V_{2}Y_{12}}}} \\{{\frac{K}{C_{2}}{\int{{I_{z2}(z)}{z}}}} = {{V_{1}Y_{21}} + {V_{2}Y_{22}}}}\end{matrix} & (18)\end{matrix}$

[0062] which can be rearranged to $\begin{matrix}\begin{matrix}{{\int{{I_{z1}(z)}{z}}} = {{\frac{C_{1}}{K}V_{1}Y_{11}} + {\frac{C_{1}}{K}V_{2}Y_{12}}}} \\{{\int{{I_{z2}(z)}{z}}} = {{\frac{C_{2}}{K}V_{1}Y_{21}} + {\frac{C_{2}}{K}V_{2}Y_{22}}}}\end{matrix} & (19)\end{matrix}$

[0063] This equation can be simplified further by making substitutionsof the type $\begin{matrix}{T_{11} = {\frac{C_{1}}{K}Y_{11}}} & (20)\end{matrix}$

[0064] which can be written (using equation 14) as $\begin{matrix}{T_{11} =  {\frac{C_{1}}{K} \cdot \frac{I_{1}}{V_{1}}} |_{V_{2 = 0}}} & (21)\end{matrix}$

[0065] From equation 19 it can be seen that, by setting V₂=0 and V₁ to1V, this is equivalent to

T ₁₁ =∫I _(z1)(z)dz| _(V) ₂ ₌₀  (22)

[0066] In a similar manner, a complete set of T matrix equations can bedefined: $\begin{matrix}{T_{11} = { {\frac{C_{1}}{K}Y_{11}{\int_{\quad}^{\quad}{{I_{z1}(z)}\quad {z}}}} \middle| {}_{{V_{1} = 1},{V_{2} = 0}}T_{12}  = { {\frac{C_{1}}{K}Y_{12}{\int_{\quad}^{\quad}{{I_{z1}(z)}\quad {z}}}} \middle| {}_{{V_{1} = 0},{V_{2} = 1}}T_{21}  = { {\frac{C_{2}}{K}Y_{21}{\int_{\quad}^{\quad}{{I_{z2}(z)}\quad {z}}}} \middle| {}_{{V_{1} = 1},{V_{2} = 0}}T_{22}  =  {\frac{C_{2}}{K}Y_{22}{\int_{\quad}^{\quad}{{I_{z2}(z)}\quad {z}}}} |_{{V_{1} = 0},{V_{2} = 1}}}}}} & (23)\end{matrix}$

[0067] Each term in the above equation represents an integral equivalentto a term in the admittance matrix Y of equation 14. From equations 16,19 and 23, the electric fields are given in terms of the voltages andthe T parameters as $\begin{matrix}{{\frac{E_{1}}{K} = {{T_{11}V_{1}} + {T_{12}V_{2}}}}{\frac{E_{2}}{K} = {{T_{21}V_{1}} + {T_{22}V_{2}}}}} & (24)\end{matrix}$

[0068] The constant factor K can be ignored, since it is only therelative amplitudes of the fields that are of concern for determiningthe radiation pattern. The above equations can then be written in matrixform as

[E]=[T][V]  (25)

[0069] This equation can be normalised further such that one of the Efield values is unity, again without altering the required result. Forpoint sources, the [E] matrix represents the field ratios, or relativecurrents fed to each element.

[0070] All the parameters in equation 25 are complex. The equationprovides a relationship between the current amplitudes and phases ofpoint sources (field ratios) and the complex voltages necessary toproduce the same response from a linear array 200. To evaluate thisrelation it is necessary to compute the complex integral of the currentdistribution on each element when the other element is short-circuited,thereby obtaining the [T] matrix. In practice this can readily be doneusing a standard computer program, for example the well-known NEC(Numerical Electromagnetics Code) or the High Frequency StructureSimulator (HFSS) available from Ansoft Corporation.

[0071] Once the [T] matrix has been found it can be inverted to obtainthe required voltages, from the equation

[V]=[T]⁻¹[E]  (26)

[0072] The analysis above shows how the field ratios determined from apoint source analysis can be replicated in a vertically-orientatedlinear array 200. This enables the horizontal radiation patterns of alinear array to be synthesised in a straightforward manner using a pointsource analysis, and enabling near-zero correlation from antennas havinga spacing much closer than is possible by simple application of Clarke'sspatial correlation formula.

[0073] One further aspect of the use of linear antennas requiresattention. In the derivation of the gain and envelope correlationcoefficient above, only the horizontal radiation patterns wereconsidered.

[0074] For vertically-orientated elements, such as those consideredabove, the radiation pattern can be obtained by straightforward patternmultiplication as

E ₁ =E ₁(φ)E ₁(θ)  (27)

[0075] which is sufficient to enable the gain to be calculated. For thecorrelation coefficient ρ_(e), because of the pure verticalpolarisation, equation 10 can be written as $\begin{matrix}{\rho_{e} = \frac{{{\int_{\Omega}^{\quad}{E_{1\theta}E_{2\theta}^{*}p_{\theta}\quad {\Omega}}}}^{2}}{\int_{\Omega}^{\quad}{E_{1\theta}E_{2\theta}^{*}p_{\theta}\quad {\Omega}{\int_{\Omega}^{\quad}{E_{2\theta}E_{2\theta}^{*}p_{\theta}\quad {\Omega}}}}}} & (28)\end{matrix}$

[0076] Substitution of equation 27 into equation 28 gives rise to termsof the type $\begin{matrix}{\int_{\Omega}^{\quad}{{E_{1}(\varphi)}{E_{1}(\theta)}{E_{2}^{*}(\varphi)}{E_{2}^{*}(\theta)}{p( {\theta,\varphi} )}\quad \sin \quad \theta {\theta}{\varphi}}} & (29)\end{matrix}$

[0077] If the angle of arrival probabilities in θ and φ can beconsidered independent, which in practice is a realistic assumption,this equation simplifies to $\begin{matrix}{\int_{\varphi}^{\quad}{{E_{1}(\varphi)}{E_{2}^{*}(\varphi)}{p(\varphi)}\quad {\varphi}{\int_{\theta}^{\quad}{{E_{1}(\theta)}{E_{2}^{*}(\theta)}{p(\theta)}\quad \sin \quad \theta {\theta}}}}} & (30)\end{matrix}$

[0078] Further, if E₁(θ)=E₂(θ), i.e. if the elements are the same, the θdependence cancels out on substitution in equation 28. Under suchcircumstances, the envelope correlation coefficient ρ_(e) is independentof the vertical radiation patterns.

[0079] The theoretical analysis above will now be applied to a practicalexample. Consider two half wave dipoles 204 a,204 b separated by 3.966cm (electrically 90° or a quarter of a wavelength at 1890 MHz), andphased to provide oppositely-directed beams. It can be seen from FIG. 6that the appropriate spacing for decorrelated beams at this spacing is125°, i.e. the elements have field ratios (or equivalent point sourcecurrents) of

E₁=1∠0

E₂=1∠125  (31)

[0080] It can also be seen from FIG. 4 that the expected gain in thehorizontal plane is approximately 4 dB. Combined with the dipole gain of2.2 dB, a total gain of 6.2 dB (relative to an isotropic radiator) canbe expected. The normalised point source radiation pattern produced bythis combination, given by equation 8, is shown in FIG. 7. In thisfigure, the direction φ=0 corresponds to the direction of the positive xaxis, and the magnitude of the radiation in a particular direction is indB relative to an isotropic radiator.

[0081] It is now required to replicate this pattern using the twodipoles 204 a,204 b. The first step is to run a program, such as NEC orHFSS, as many times as there are sources, with 1V applied to the sourcein question and all the other sources shorted. For each run the currentson each radiator should be integrated (achieved in NEC by adding realand imaginary components for each equal length segment), giving theelements of the [T] matrix.

[0082] For two 1 mm diameter half wavelength dipoles 204 a,204 b,separated by a quarter of a wavelength at a frequency of 1890 MHz, suchsimulations show that

T ₁₁=9.84−j9.64=T ₂₂

T ₁₂=3.02+j6.99=T ₂₁  (32)

[0083] Now that [E] and [T] are known, the dipole feed voltages can befound, using equation 26, as

V ₁=47.30−j65.68

V ₂=−28.09+j1.98  (33)

[0084] Note that the normalised voltage ratio, of 0.35∠130, is verydifferent from the field ratio, of 1∠125.

[0085] Using these voltages as the feeds for the dipole elements 204a,204 b gives the radiation pattern shown in FIG. 8 (generated fromNEC). The radiation patterns are also shown at 1700 MHz (dashed) and2080 MHz (chain dashed) to show the radiation pattern variation over a20% fractional bandwidth. This demonstrates that reasonable bandwidthcan be achieved in an antenna diversity arrangement made according tothe present invention.

[0086] The radiation pattern at 1890 MHz, shown by the solid curve inFIG. 8, corresponds closely to that in FIG. 7, generated by simple pointsource theory.

[0087] The impedances of the two antenna elements were found to be

Z ₁=106.6+j115.8

V ₂=32.8+j37.1  (34)

[0088] These impedances should be taken into account in the design ofany power splitting and phasing circuitry 206. FIG. 9 is a Smith chartshowing the impedance of the first antenna 204 a over a 20% bandwidth(i.e. 1700 to 2080 MHz), which demonstrates that such an array canpotentially have a very good bandwidth.

[0089] The description above has shown that the radiation patterns andcorrelation of vertically orientated linear antennas can be simulatedusing point sources and then realised in practice via a numericaltransform. However, so far it has been necessary for all the antennas tobe fed.

[0090] In many cases a good approximation to the patterns with allantennas fed can be obtained by the use of parasitic elements.Impedances with low real values can often be replaced effectively by(lossless) parasitic reactances that are conjugate to the reactive partof the impedance. Near correct feed voltages are then set up by mutualinteractions between the antennas.

[0091] Using the same example as above, this principle can beillustrated by replacing the feed to the second antenna element 204 bwith a parasitic reactance of −37.1 Ohms. The resulting radiationpatterns (with the lines having the same meanings as in FIG. 8, areshown in FIG. 10. Even though the second element 204 b did not meet thecriterion of having a low real impedance (compared to its reactance),the radiation patterns are in reasonable agreement with those of FIG. 8.In practice it has been found that varying the parasitic reactancearound the complex conjugate of the fed reactance can often result inbetter radiation patterns.

[0092] The description above has concentrated on the provision ofdirectional antenna patterns from an array 200. However,omni-directional operational modes can also be provided in the same way,by setting the point source contribution of an unused antenna to zeroand performing the transformation. This will give feed voltages thatresult in no radiation from one of the elements. Parasitic loading canthen be used to avoid the need to feed the unused antenna.

[0093] Although the present invention has been described in relation tolinear electric antennas 204 a,204 b it is applicable to any antennawhich can be linearised. For example, it would be possible to use theabove methods to analyse the θ radiation from a sloping antenna. Theterms “horizontal” and “vertical” have been employed in the descriptionbecause many radio communication systems employ vertical antennas 204a,204 b to generate vertically polarised radiation. However, in generalthe term “vertical” should be understood to mean a direction parallel tothe intended polarisation direction of the radiation, while the term“horizontal” should be understood to mean a direction perpendicular tothe intended polarisation direction.

[0094] Although the description above related to an antenna diversityarrangement 200 having two antennas 204 a,204 b, it will be apparent tothe skilled person that it is equally applicable to arrangements havingmore antennas.

[0095] From reading the present disclosure, other modifications will beapparent to persons skilled in the art. Such modifications may involveother features which are already known in the design, manufacture anduse of antenna diversity arrangements, and which may be used instead ofor in addition to features already described herein. Although claimshave been formulated in this application to particular combinations offeatures, it should be understood that the scope of the disclosure ofthe present application also includes any novel feature or any novelcombination of features disclosed herein either explicitly or implicitlyor any generalisation thereof, whether or not it relates to the sameinvention as presently claimed in any claim and whether or not itmitigates any or all of the same technical problems as does the presentinvention. The applicants hereby give notice that new claims may beformulated to such features and/or combinations of features during theprosecution of the present application or of any further applicationderived therefrom.

[0096] In the present specification and claims the word “a” or “an”preceding an element does not exclude the presence of a plurality ofsuch elements. Further, the word “comprising” does not exclude thepresence of other elements or steps than those listed.

1. An antenna diversity arrangement comprising a plurality of antennasand means for feeding each of the plurality of antennas with a signal ofsuitable amplitude and phase to enable the generation of a plurality ofantenna beams, wherein the correlation coefficient between any pair ofbeams is substantially zero.
 2. An arrangement as claimed in claim 1,characterised in that the amplitude and phase of the signal feeding eachantenna is predetermined.
 3. An arrangement as claimed in claim 1 or 2,characterised in that the amplitudes of all the feed signals aresubstantially equal.
 4. An arrangement as claimed in claims 1 or 2,characterised in that the diversity arrangement comprises two antennas.5. An arrangement as claimed in claim 4, characterised in that the phasedifference between the feed signals of an equivalent point sourceantenna diversity arrangement is substantially equal to cos⁻¹(−J₀(kd)),where kd is the electrical spacing of the antennas.
 6. A wireless deviceincorporating an antenna diversity arrangement as claimed in claim 1 or2.
 7. A wireless device incorporating an antenna diversity arrangementas claimed in claim
 3. 8. A wireless device incorporating an antennadiversity arrangement as claimed in claim
 4. 9. A wireless deviceincorporating an antenna diversity arrangement as claimed in claim 5.10. A method of operating an antenna diversity arrangement comprising aplurality of antennas, the method comprising feeding each of theplurality of antennas with a signal of suitable amplitude and phase toenable the generation of a plurality of antenna beams, wherein thecorrelation coefficient between any pair of beams is substantially zero.11. A method as claimed in claim 10, characterised by the amplitude andphase of the signal feeding each antenna being predetermined.
 12. Amethod as claimed in claim 10 or 11, characterised by the amplitudes ofall the feed signals being substantially equal.
 13. A method as claimedin claims 10 or 11, characterised by the diversity arrangementcomprising two antennas and by the phase difference between the feedsignals of an equivalent point source antenna diversity arrangementbeing substantially equal to cos⁻¹(−J₀(kd)), where kd is the electricalspacing of the antennas.